1. Field of the Invention
The present invention relates to seismic data processing for analysis of subsurface formation structure, and in particular to an iterative dip-steering median filter for such processing.
2. Description of the Related Art
Noise attenuation has been important in seismic data processing for producing more accurate representations of the results of seismic surveys in areas of interest. Enhancement of the signal to noise ratio in pre-stack gathers of the seismic data can result in better subsequent processing, imaging and interpretation.
A number of signal processing techniques have been employed in efforts to suppress noise. These techniques have been categorized into three main groups: frequency-space (f-x) domain prediction filtering, the singular value decomposition (SVD) method and median filtering.
Random noise attenuation by predictive deconvolution in the f-x domain was introduced some years ago. F-x deconvolution has been based on the assumption that the spatial signals at each single frequency are composed of a sum of a limited number of complex harmonics. In the presence of noise, autoregressive models are suitable to predict a super-position of harmonics. F-x deconvolution was effective in attenuating random noise and could handle events with what are known as conflicting dips. Conflicting dips refer to situations where the seismic data indicate more than one likely dip might be present. However, f-x deconvolution has been known to distort signal levels significantly when extremely strong noise exists. It has thus been proposed to adopt projection filters instead of the predictive filter.
Singular value decomposition (SVD) has been another tool to enhance laterally coherent events in seismic gathers. Singular value decomposition forms a data-covariance matrix before employing an eigenvalue decomposition to extract the coherent events. SVD can effectively suppress random noise by summing only the contributions of the largest singular values, which represent the laterally coherent signals. Expanded SVD applications have been used for seismic data in the f-x domain.
Median filtering has also been widely accepted in the oil and gas industry. An article: Bednar, J. B., 1983, “Applications of median filtering to deconvolution, pulse estimation, and statistical editing of seismic data”, Geophysics, 48, 1598-1610, discussed some applications of median filtering in seismic prospecting. An article: Duncan, G., and G. Beresford, 1995, “Some analyses of 2D median f-k filters”, Geophysics, 60, 1157-1168, introduced a 2D median f-k filter which used the coefficients of a truncated impulse response of an f-k filter as the weight coefficients for the weighted median process. An article: Zhang, R., and T. J. Ulrych, 2003, “Multiple suppression based on the migration operator and a hyperbolic median filter”, SEG, Expanded Abstracts, 1949-1952, discussed use of a hyperbolic median filter to suppress multiples, while an article by Liu, C., Y. Liu, B. Yang, D. Wang, and J. Sun, 2006, “A 2D multistage median filter to reduce random seismic noise”, Geophysics, 71, V105-V110 adapted a 2D multistage median filter to suppress the random noise in land seismic data. An article by Liu, Y., Y. Luo, and Y. Wang, 2009, “Vector median filter and its Applications in Geophysics”, SEG, Expanded Abstracts, 29, 3342-3346, proposed to apply a vector median filter (VMF) in geophysics. An article by Huo, S., Luo, Y., and P. G. Kelamis, 2009, “Simultaneous sources separation via multi-directional vector-median filter” SEG Expanded Abstracts 28, 31-35, discussed expansion of the vector median filter to a multi-directional vector median filter (MD-VMF) for the purpose of separating blended field seismic data.
Median filter processing has assumed that coherent events have been flattened beforehand, while MD-VMF filtering assumed that there was a single dip in the operation window. Therefore, so far as is known, neither the median filter nor the multi-directional vector median filter method could, so far as is known, handle a seismic gather with conflicting dips.
The technique known a frequency-wavenumber (or F-K) filtering was used when the seismic data indicated conflicting dips. Experience has shown that a frequency-wavenumber filter was not an edge-preserving filter and had edge effects after filtering. An F-K filter did not perform satisfactorily in eliminating spike or impulse noise. As noted above, a median filter, being an edge-preserving filter, was typically suitable for attenuating spike noise, but could only work on flattened events.